An Australian man is believed to be responsible for a suicide bombing that killed at least five people and injured 90 in Baghdad on Thursday, marking the incident as the first committed by an Australian in Iraq.

The Islamic State of Iraq, dubbed a terrorist group by the Australian government, reported via Twitter that a man called Abu Bakr al-Australi detonated explosives in a market place in the heart of the Iraq city.

'Abu Bakr Al Australi may Allah accept him targets a Shiite temple the Militias use as HQ & Kills and injures 90 militiamen,' the original tweet read.

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An Australian man is believed to be responsible for a suicide bombing that killed at least five people and injured 90 in Baghdad on Thursday

A statement released by the terrorist group, refereed to the man as a 'hero' and a 'martyr'.

A man naming himself AbuHafs D Australian on Twitter, confirmed the report saying: 'Abu Bakr al-Australi (the Australian) had detonated explosives in a vest he was wearing near the mosque.'

Subsequent reports by Al-Jazeera, issued a different account of the events in which the news-agency quoted a local police officer who claimed that the explosives had been hidden on a wooden cart.

Al-Australi is often used at the end of jihadist names to identify the person as coming from Australia.

The incident comes only a week after the Australian government officially named the Islamic State group as a terrorist organisation, and clarifying that citizens intending to join, fight with or fund a listed terrorist groups in Iraq or Syria could face up to 25 years in jail.

Attorney General, George Brandis, also revealed details about the number of Australians believed to be supporting extremist groups at a press conference earlier this week.

'There are probably about 60 Australians in Syria fighting for one side or the other but predominantly the anti- government side, and an alarming number of those people are gravitating towards the Al-Qaeda off-shoot,' Mr Brandis said.

'We have some 10s of people who have already returned and we have probably another 150 who we are looking at here in Australia who have inclinations to support those two extremist movements.'

In a statement on Friday, Mr Brandis commented on the alleged suicide bombing in Iraq.

'If correct, this is a disturbing development and is a further example of the dangerous and volatile situation in Iraq at present. This would be the second Australian suicide bomber in the Iraq and Syria conflicts,' he said.

'The Government deplores the violent actions being undertaken by ISIL and other extremist groups in Iraq and Syria, and is deeply concerned about the involvement of Australians in these activities.

'As I have said many times, it is illegal for Australians to engage in the conflicts in Iraq and Syria and the Government urges Australians not to travel to the region.

'The participation by Australians in the conflict in Iraq and Syria poses a significant domestic security threat to Australia when those involved return home and seek to pursue violence here.

'The Government will continue to take all necessary measures to keep Australia and Australian interests safe.'

Late last year, a Queensland man was reportedly behind another suicide bombing in Syria while fighting for the terrorist group the al-Nusrah Front.